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The Well-Posedness and Ergodicity of a CIR Equation Driven by Pure Jump Noise

Author

Listed:
  • Xu Liu

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Xingfu Hong

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Fujing Tian

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Chufan Xiao

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

  • Hao Wen

    (China Aerodynamics Research and Development Center, Mianyang 618000, China)

Abstract

The current paper is devoted to the dynamical property of the stochastic Cox–Ingersoll–Ross (CIR) model with pure jump noise, which is an extension of the CIR model. Firstly, we characterize the existence and 2-moment of the CIR process with a pure jump process. Consequently, we provide sufficient conditions for the compensated Poisson random measure under which the CIR process with a pure jump process is ergodic. Moreover, the stationary solution can be constructed from the invariant measure. Some numerical simulations are provided to visualize the theoretical results.

Suggested Citation

  • Xu Liu & Xingfu Hong & Fujing Tian & Chufan Xiao & Hao Wen, 2025. "The Well-Posedness and Ergodicity of a CIR Equation Driven by Pure Jump Noise," Mathematics, MDPI, vol. 13(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1938-:d:1676153
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    References listed on IDEAS

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